Simplify the following expression: $ p = \dfrac{-7}{n - 10} - \dfrac{1}{9} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9}{9}$ $ \dfrac{-7}{n - 10} \times \dfrac{9}{9} = \dfrac{-63}{9n - 90} $ Multiply the second expression by $\dfrac{n - 10}{n - 10}$ $ \dfrac{1}{9} \times \dfrac{n - 10}{n - 10} = \dfrac{n - 10}{9n - 90} $ Therefore $ p = \dfrac{-63}{9n - 90} - \dfrac{n - 10}{9n - 90} $ Now the expressions have the same denominator we can simply subtract the numerators: $p = \dfrac{-63 - (n - 10) }{9n - 90} $ Distribute the negative sign: $p = \dfrac{-63 - n + 10}{9n - 90}$ $p = \dfrac{-n - 53}{9n - 90}$